When should I create a custom loss function?
Using two value and using MSE is probably a better approach. I'd you combine the value to one value, like the case of summation, the network may fits to output 0 on one axis and the value on the other. The method you propose also have the same issue. There are many combination to the real distance, but only one is correct. 
For a neural network to learn faster, one value will not help it learn faster. Instead, accuracy is often increased if the predicted value is a one hot vector of labels instead of a single value. Hope this can help you.